Correlation Analysis: Predictor and Criterion Variables

This article provides a detailed solution for correlation analysis of predictor and criterion variables with solved examples. It explains the significance of correlation coefficient and hypothesis testing. The predictor variables include Scale of Emotional Intelligence, Intrinsic Motivation Inventory, and Number of Absences, while the criterion variables include Aggression Questionnaire, Maths Score, and Grades.

CORRELATION
Assignment 8
[Pick the date]
Student Name

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Solution
1. Predictor variable
The independent variable (X) is termed a predictor variable and hence, Scale of Emotional
Intelligence (SEI) would be the predictor variable.
2. Criterion variable
The dependent variable (Y) is termed a criterion variable and hence, Aggression Questionnaire
(AQ) would be criterion variable.
3. Correlation
a. Hypotheses
Null hypothesis Ho : ρ=0
Alternative hypothesis H1 : ρ≠ 0
b. Le the level of significance = 5%
Degree of freedom ¿ n−1=20−1=19
Critical value of t stat for two tailed test = ± 2.093
c. Test statistic
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n=20
t= r √n−2
√1−r 2 =−0.9448 √20−2
√0.10735 =−12.23
The value of t stat = -12.23
d. It is apparent that calculated t stat does not lie between the two critical values and therefore,
sufficient evidence is present to reject the null hypothesis and accept the alternative
hypothesis.
4) The effect of emotional intelligence is significant on aggression level as the correlation
coefficient is significant. Also, there is a negative relationship between the two which implies
that the higher the scale of emotional intelligence a person has, the lower would be the
aggression level.
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Solution
1. Predictor variable
The independent variable (X) is termed a predictor variable and hence, Intrinsic Motivation
Inventory (IMI) would be the predictor variable.
2. Criterion variable
The dependent variable (Y) is termed a criterion variable and hence, Maths Score would be
criterion variable.
3. Correlation
a. Hypotheses
Null hypothesis Ho : ρ=0
Alternative hypothesis H1 : ρ≠ 0
b. Level of significance = 5%
Degree of freedom ¿ n−1=22−1=21
Critical value of t stat for two tailed test = ± 1.748
c. Test statistic
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n=22
t= r √n−2
√1−r 2 = 0.83264 √22−2
√0.3067 =6.7237
The value of t stat = 6.7237
d. It is apparent that calculated t stat does not lie between the two critical values and therefore,
sufficient evidence is present to reject the null hypothesis and to accept the alternative
hypothesis.
4) The effect of motivation on math score is significant as the correlation coefficient is
significant. Also, there is a positive relationship between the two which implies that the higher
the motivation level of a student the higher would be their maths score.
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Solution
1. Predictor variable
The independent variable (X) is also known as a predictor variable and hence, Number of
Absence would be the predictor variable.
2. Criterion variable
The dependent variable (Y) is termed a criterion variable and hence, Grades would be criterion
variable.
3. Correlation
a. Hypotheses
Null hypothesis Ho : ρ=0
Alternative hypothesis H1 : ρ≠ 0
b. Level of significance = 5%
Degree of freedom ¿ n−1=26−1=25
Critical value of t stat for two tailed test = ± 1.735
c. Test statistic
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n=26
t= r √ n−2
√ 1−r 2 = 0.83264 √ 26−2
√ 0.3067 =−7.655
The value of t stat = -7.655
d. It is apparent that calculated t stat does not lie between the two critical values and therefore,
sufficient evidence is present to reject the null hypothesis and to accept the alternative
hypothesis.
4) It is apparent from the above hypothesis testing that the correlation coefficient is significant
which implies that the relationship between number of absences and the grade is significant.
Further, considering the negative value of the correlation coefficient, hence the higher the
number of absences, the lower would be the grade of the students.
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